Question

The graph of a linear function is shown.

A coordinate plane with a straight line passing through (negative 4, 2), (0, 0), and (4, negative 2).
Which word describes the slope of the line?

positive
negative
zero
undefined

Answer 1

The slope of a line is determined by the rise over run, which is the change in the y-coordinates divided by the change in the x-coordinates between two points on the line.

Given the points \((-4, 2)\), \((0, 0)\), and \((4, -2)\):

1. Look at the points \((0, 0)\) and \((4, -2)\):

- The change in \(y\) (rise): \(-2 - 0 = -2\)
- The change in \(x\) (run): \(4 - 0 = 4\)

So, the slope \(\frac{\text{rise}}{\text{run}} = \frac{-2}{4} = -\frac{1}{2}\).

Since the slope is \(-\frac{1}{2}\), it is **negative**.

Therefore, the word that describes the slope of the line is **negative**.